Problem: A geometric sequence of positive integers is formed for which the first term is 3 and the fourth term is 192. What is the third term of the sequence?
Explanation: Let the geometric sequence have common ratio $r$. We know that $3\cdot r^3=192$, or $r=4$. Thus, the third term is $3 \cdot r^2 = 3 \cdot 4^2 = \boxed{48}$.